When a fire or internal combustion engine gives off noxious fumes, the further you are from the source, the lower the concentration and the longer it takes for any portion to reach you. When you heat a metal on one end, it takes a while for that heat to reach the other end with smaller effects taking place further away. When a river enters into a lake, the linear motion of the water quickly dissipates.
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Would you be surprised to find that a simple mathematical expression describes all of these phenomena?
The way that heat moves through a solid along with the way in which a gas or aerosol mixes when released into air follow the same rules for dilution. In nerdy speak, when heat transport occurs in a solid material and pollution mixes in air, these spread out using identical mathematical constructs for the measured values. Even a flow of liquid into a stationary volume will see its momentum dispersed in the same way. The rules all these follow is often referred to as diffusion. Yep, simple diffusion.
Air pollutants being distributed in the atmosphere and the heat from any point in a material move in such a way as to approach a constant value, they try to average out over the entire volume. The detailed mathematics requires calculus but the basic interpretation is that the transport always distributes in such a way as to even out the overall concentration. The larger the mixing volume used, the smaller the final average concentration. This is also just a form of the second law of thermodynamics, that disorder always increases. This second law will continue to increase disorder until everything everywhere attains the same value of energy and concentration.
To see how heat travels through a solid, it is just simple vibrations. Here, the atoms of the material are all attached to all their adjacent bonded atoms with springs. The atomic bonds holding together all materials in solid form are indeed springs in terms of their behavior.
If all the atoms were perfectly still at a temperature of zero degrees Kelvin and any one single atom were be forced to move, this moving atom would then push and pull its nearest neighbors. The reaction from these nearest neighbors is then to push and pull a little weaker on their nearest neighbors and so on. These vibrations would then slowly move out eventually causing some motion on all the atoms in the whole substance. The distribution of these vibrations moving out in three dimensions is diffusion.
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